Problem: Simplify the following expression: $k = \dfrac{15r - 20p}{20r - 15p} - \dfrac{10q + 20p}{20r - 15p}$ You can assume $p,q,r \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{15r - 20p - (10q + 20p)}{20r - 15p}$ $k = \dfrac{15r - 40p - 10q}{20r - 15p}$ The numerator and denominator have a common factor of $5$, so we can simplify $k = \dfrac{3r - 8p - 2q}{4r - 3p}$